scholarly journals Commutators of potential type operators with Lipschitz symbols on variable Lebesgue spaces with different weights

2019 ◽  
pp. 855-883
Author(s):  
Luciana Melchiori ◽  
Gladis Pradolini ◽  
Wilfredo Ramos
Keyword(s):  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces ◽  
Potential Type ◽  
Potential Type Operators

scholarly journals A weighted inequality for potential type operators

2019 ◽  
Vol 10 (4) ◽  
pp. 413-426
Author(s):  
Aïssata Adama ◽  
Justin Feuto ◽  
Ibrahim Fofana
Keyword(s):  
Convolution Type ◽  
Weighted Inequality ◽  
Lebesgue Spaces ◽  
Potential Type ◽  
Type Spaces ◽  
Weak Lebesgue Spaces ◽  
Potential Type Operators

AbstractWe establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on {\mathbb{R}} endowed with a measure which needs not to be doubling.

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

The Calderón operator and the Stieltjes transform on variable Lebesgue spaces with weights

2019 ◽  
Vol 71 (3) ◽  
pp. 443-469
Author(s):  
David Cruz-Uribe ◽  
Estefanía Dalmasso ◽  
Francisco J. Martín-Reyes ◽  
Pedro Ortega Salvador
Keyword(s):  
Stieltjes Transform ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces

Boundedness of integral operators associated with the Kontorovich–Lebedev transform in the Lebesgue spaces type

2020 ◽  
pp. 2150081
Author(s):  
Anis Kroumi
Keyword(s):  
Riesz Potential ◽  
Integral Operators ◽  
Type Operator ◽  
Maximal Operators ◽  
Lebesgue Spaces ◽  
Potential Type

In this paper, we prove the boundedness for the maximal and fractional maximal operators and Riesz potential-type operator associated with the Kontorovich–Lebedev transform (KL transform)in the [Formula: see text] spaces.

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